Hamilton was the son of Henry Hamilton, member of the British Parliament for Donegal, County Cork, Ireland. Young Henry grew up in Cork, and was later commissioned into the 15th Regiment of Foot in the British Army. During the French and Indian War (1754–1760), he won distinction at the battles of Louisburg and Quebec, both British victories.

In 1775 Hamilton became the British Lieutenant Governor at Detroit. He fostered good relations between the British and the Indians in the Old Northwest, the territory south and west of the Great Lakes comprising the present-day states of Ohio, Indiana, Illinois, Michigan, Wisconsin, and part of Minnesota. During the American Revolution, American settlers in the area were vulnerable to attack by the British and the Indians. Hamilton became known as the “hair buyer” for his rumored practice of paying bounties to the Indians for American scalps. Modern historians have largely discounted this as legend, however.

In Aug. 1778, Hamilton learned of a planned attack on British outposts by volunteers from Virginia under Gen. George Rogers Clark. Hamilton mounted an expedition to drive the Virginians back, but on Feb. 25, 1779, he was forced to surrender Fort Sackville at Vincennes. Hamilton was captured and imprisoned at Williamsburg, Va., until he was released in a prisoner exchange in 1781. He later served as lieutenant governor of Quebec (1782–1785), lieutenant governor and then governor of Bermuda (1785–1794), and governor of Dominica (1794–1796).

In 1795, at the age of 61, Hamilton married 25-year-old Elizabeth Lee. The couple had one child, Mary Anne Pierpoint Hamilton.